Anomalous surfaces of fracton phases

Fractons are three-dimensional phases distinguished by the restricted mobility of their quasiparticles, and share many similarities to topological order in two dimensions. In this talk, we demonstrate that boundaries of well-known fracton models feature anomalous constraints arising from the emergent conservation laws that govern the bulk fracton order, in a manner similar to 2D topological orders such as the toric code. These constraints restrict the allowed boundary operators to those that commute with certain subsystem symmetry operations, determined both by the bulk fracton order and the direction of boundary termination. The constraints are anomalous in the sense that they cannot arise in any 2D local theory; we demonstrate this from a microscopic perspective, showing that the boundary operators' anticommutation relations are inconsistent with the constraints in any such theory. This gives rise to a rich phase diagram for the boundary theory, in correspondence with that of local 2D subsystem-symmetric systems.